I've been reading through A Smarter Way to Find Pitch, describing its pitch detection algorithm using autocorrelation.

I've been having trouble understanding the accuracy claims. It says:

MPM runs in real time with a standard 44.1 kHz sampling rate. It operates without using low-pass filtering so it can work on sound with high harmonic frequencies such as a violin and it can display pitch changes of one cent reliably.

I cannot fathom how detecting changes of one cent is possible. Considering a note played at 441Hz, sampled at 44.1kHz, one would measure a first peak at tao=100 samples (delay space).

The next closest note which could be measured, by my understanding, would have a peak at the 101st sample. This would be a frequency of 437Hz, or about 16 cents lower than the first note. What am I missing here?